The generator matrix

 1  0  0  1  1  1  0  1  X X^2  1  1 X^2+X  1  1 X^2  1  X  1  X  1  1  1  X X^2  1  1  X  1  1 X^2+X  1 X^2+X  1  1  X  1  1  0 X^2+X  1  1  1 X^2 X^2  0 X^2  1 X^2  1  0  X  1  1  1  X  1 X^2+X  1  1  1  1  0  X  1  1  X  0  0  1  1  1  1  1  1  0  0 X^2+X  1  1  1  1 X^2  1
 0  1  0  0  1  1  1  X  1 X^2+X X^2+X X^2+1  1 X+1 X^2  1 X^2+X+1  0 X+1  1 X^2  1 X^2+X+1 X^2+X  1  X X^2+X  1  0 X^2  1 X+1  1  1 X^2+X+1 X^2+X X^2+X X^2+X+1  1  1 X^2+1 X^2 X+1 X^2+X  1 X^2  1 X^2+X  1 X+1  1  1 X^2 X^2+X X^2  1  0 X^2 X^2+X X+1 X^2+1 X^2  1  1 X+1  0  X  1  1 X^2  X  1  1 X^2+X+1 X^2+X  1  1  1 X^2 X^2+X+1  1  1  X X^2
 0  0  1 X+1 X^2+X+1  0 X+1  1 X^2  1  0  1  1  0 X^2+1  X  1  1 X^2+X X+1  X  X X^2+X+1  1 X^2+1 X^2+X X^2+X+1  X X^2+1 X^2+X X^2+X+1 X^2  0 X^2+X+1  X  1 X^2+1  1 X^2  1 X^2+X X^2 X^2+X+1  1  1  1 X^2+X+1  0 X^2 X^2+X  0  X X+1 X^2+X X^2  0  0  1 X^2+1 X^2+X+1 X^2+X X^2+X  X X^2+X  1 X^2+X+1  1 X+1 X^2+1  0 X^2+X X^2+1  X X+1  0 X+1 X^2+X+1 X^2+X+1 X^2 X^2+X+1 X^2+1 X^2  1  X
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0  0

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+70x^77+260x^78+312x^79+387x^80+356x^81+419x^82+284x^83+404x^84+216x^85+277x^86+162x^87+220x^88+192x^89+158x^90+110x^91+114x^92+46x^93+30x^94+22x^95+24x^96+12x^97+7x^98+6x^99+2x^100+4x^101+1x^102

The gray image is a linear code over GF(2) with n=336, k=12 and d=154.
This code was found by Heurico 1.16 in 1.24 seconds.